5.1 Special Right Triangles

Slides:

Advertisements

Similar presentations

Special Right Triangles Chapter 7.4. Special Right Triangles triangles triangles.

Advertisements

The Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.

Pythagorean Theorem By: Tytionna Williams.

Unit 7 Part 2 Special Right Triangles 30°, 60,° 90° ∆s 45°, 45,° 90° ∆s.

10.5 – The Pythagorean Theorem. leg legleg hypotenuse hypotenuse leg legleg.

5.1 Special Right Triangles. What you should already know… Right triangles have one 90 o angle The longest side is called the HYPOTENUSE  It is directly.

MM2G1. Students will identify and use special right triangles.

7-3 Special Right Triangles

30°, 60°, and 90° - Special Rule The hypotenuse is always twice as long as the side opposite the 30° angle. 30° 60° a b c C = 2a.

Warmup:Solve for y. 8.2 Special Right Triangles LEQ: What are special right triangles and how do we use them?

Geometry Section 7.4 Special Right Triangles. 45°-45°-90° Triangle Formed by cutting a square in half. n n.

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle.

4.6 Congruence in Right Triangles In a right triangle: – The side opposite the right angle is called the hypotenuse. It is the longest side of the triangle.

8.2 Special Right Triangles

30  - 60  - 90  Triangles And You! Remember the Pythagorean Theorem? The sum of the square of the legs is equal to the square of the hypotenuse. a.

8.2 Special Right Triangles. Side lengths of Special Right Triangles Right triangles whose angle measures are 45°-45°-90° or 30°- 60°-90° are called special.

11.4 Pythagorean Theorem Definitions Pythagorean Theorem

8.2 Special Right Triangles

8-3 Special Right Triangles You used properties of isosceles and equilateral triangles. Use the properties of 45°-45°-90° triangles. Use the properties.

4.4 Pythagorean Theorem and the Distance Formula Textbook pg 192.

Warm-up Solve the equation for the missing variable. Assume all variables are positive. Express the answer in simplified radical form. 1. c 2 =

Pythagorean Theorem Converse Special Triangles. Pythagorean Theorem What do you remember? Right Triangles Hypotenuse – longest side Legs – two shorter.

Pythagorean Theorem and Special Right Triangles. Anatomy of a Right Triangle Why is a right triangle called a right triangle? Because it is a triangle.

NOVEMBER 3, 2008 Pythagorean Theorem and Special Right Triangles.

8-2 Special Right Triangles Objective: To use the properties of and triangles.

Geometry 7-5 Areas of Regular Polygons. Review Areas.

– Use Trig with Right Triangles Unit IV Day 2.

Lesson 8-4 Special Right Triangles (page 300) Essential Question What is so special about the special right triangles?

Sect. 9.4 Special Right Triangles Goal 1 Side Lengths of Special Right Triangles Goal 2 Using Special Right Triangles in Real Life.

Pythagorean Theorem and Special Right Triangles

Special Right Triangles

Introduction to Special Right Triangles

The Distance and Midpoint Formulas

Forms of a Quadratic Equation

Special Right Triangles

8-2 Special Right triangles

Triangles Unit 3 Review Material

Midpoint And Distance in the Coordinate Plane

5.1 Special Right Triangles

12-2 The Pythagorean Theorem

7.2 The Pythagorean Theorem and its Converse

8-2 Special Right Triangles

Math 3-4: The Pythagorean Theorem

Section 5.5: Special Right Triangles

8-3 Special Right Triangles

6-3 The Pythagorean Theorem Pythagorean Theorem.

45°-45°-90° Special Right Triangle

Warmup:Solve for y.

The Pythagorean Theorem

7-4: special right triangles

Objective: To use the properties of 30°-60°-90° triangle.

Right Triangles Unit 4 Vocabulary.

Special Right Triangles

6.5 Pythagorean Theorem.

Special Right Triangles

Special Right Triangles

Special Right Triangles

Chapter 3: Solving Equations

Geometric Mean and the Pythagorean Theorem

5.1 Special Right Triangles

Special Right Triangles

The Pythagorean Theorem

Special Right Triangles

Special Right Triangles

In a right triangle, the side opposite the right angle is called the hypotenuse. This side is always the longest side of a right triangle. The other.

Warm Up April 1st What is the hypotenuse if the leg lengths are a = 72 and b = 30? Simplify 72.

7-3 Special Right Triangles

Special Right Triangles

Presentation transcript:

5.1 Special Right Triangles

What you should already know… Right triangles have one 90o angle The longest side is called the HYPOTENUSE It is directly across from the 90o The other sides are called LEGS Hypotenuse LEG

a2 + b2 = c2 Pythagorean Theorem The sides of a right triangle satisfy this theorem: a2 + b2 = c2 Hypotenuse LEG

Vocabulary 45-45-90 Triangle: In a 45-45-90 triangle, the hypotenuse is times as long as each leg.

Hints for 45-45-90 Leg to Hypotenuse: MULTIPLY by Hypotenuse to Leg: DIVIDE by Hypotenuse = LEG LEG LEG

Example 1: Find the value of x. a) b)

Vocabulary 30-60-90 Triangle: In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg.

How do you know which is the shorter leg and which is the longer leg??? We know that the hypotenuse is directly across from the 90O angle. The shorter leg is across from the smaller angle (30o) The longer leg is across from the larger angle (60O)

30-60-90 30o Hypotenuse Longer Leg 60o Shorter Leg

You always want to work with the Shorter Leg…it makes it easier! Hints for 30-60-90 Shorter Leg to Hypotenuse: MULTIPLY by 2 Hypotenuse to Shorter Leg: DIVIDE by 2 Shorter Leg to Longer Leg: MULTIPLY by Longer Leg to Shorter Leg: DIVIDE by You always want to work with the Shorter Leg…it makes it easier!

30-60-90 Shorter Leg Longer Leg = Shorter Hypotenuse = 2Shorter 30o

Example 2: Find the values of x and y.

You Try: Find the value of each variable. 1) 2)

Homework P. 153 #1-13all